Problem: Calculate the product below and give your answer in scientific notation. $ {\left(8.2\times 10^{-3} \right) \times \left(2.0\times 10^{2} \right) =\ ?} $
Explanation: Start by collecting the significands and exponents. $ ({8.2} \times {10^{-3}}) \times ({2.0} \times {10^{2}}) = ({8.2} \times {2.0}) \times ({10^{-3}} \times {10^{2}}) $ Then multiply each term separately. When multiplying exponents with the same base, add the powers together. $= {16.4} \times {10^{-3 \,+\, 2}}$ $= {16.4} \times {10^{-1}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the left without changing the value of our answer. We can use the fact that ${16.4}$ is the same as ${1.64 \times 10}$ or ${1.64 \times 10^{1}}$. $ = {1.64 \times 10^{1}} \times {10^{-1}} $ $ = 1.64 \times 10^{{1} + {-1}} $ $= 1.64\times 10^{0}$